Optical tweezers coupled to surfaces and thin solid-state membranes are very useful in a wide range of nanophotonics applications and open up new ways of measuring surface adhesion and molecular forces. A recent example is the coupling of optical tweezers to solid-state nanopore sensors for accurate control and biophysical investigation of single DNA molecules. Such membrane-integrated optical traps do, however, show a variety of optical effects that are not well understood. A major limitation in these experiments comes from periodic modulations of the bead position from the trapping plane when the optical trap is axially moved towards the membrane. While previously considered detection artifacts, it is shown here that these modulations correspond to real movements of the optical trap position that results from interference between the incident trapping laser and reflections from the thin solid-state membrane. An experimental study of these oscillations is presented, as well as optical simulations based on the finite-difference time-domain method, providing insight into the underlying interference phenomenon. Finally, an alternate measurement geometry is presented that eliminates these oscillations, specifically useful for performing optical-trap-coupled nanopore force spectroscopy.